Electro magnetism

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  • Electricityand

    MagnetismBenjamin Crowell

    Book 4 in the Light and Matter series of introductory physics textbookswww.lightandmatter.com

  • Electricity andMagnetism

  • The Light and Matter series ofintroductory physics textbooks:1 Newtonian Physics2 Conservation Laws3 Vibrations and Waves4 Electricity and Magnetism5 Optics6 The Modern Revolution in Physics

  • Electricity andMagnetism

    Benjamin Crowell

    www.lightandmatter.com

  • Light and MatterFullerton, Californiawww.lightandmatter.com

    1999-2001 by Benjamin CrowellAll rights reserved.

    Edition 2.1rev. 2001-05-06

    ISBN 0-9704670-4-4

  • To Arnold Arons.

  • 9Contents

    Brief Contents1 Electricity and the Atom....... 152 The Nucleus .......................... 413 Circuits, Part 1 ...................... 714 Circuits, Part 2 ...................... 955 Fields of Force .................... 1096 Electromagnetism .............. 127Exercises ................................................... 147Solutions .................................................... 153Glossary ..................................................... 155Index ........................................................... 157Supplements 4-7 and 4-8 are available online at

    www.lightandmatter.com.7 LRC Circuits8 Maxwell's Equations

  • 10 Contents

    ContentsPreface ......................................................... 131 Electricity and

    the Atom .....................151.1 The Quest for the Atomic Force........... 161.2 Charge, Electricity and Magnetism ...... 181.3 Atoms .................................................. 221.4 Quantization of Charge........................ 281.5 The Electron ........................................ 311.6 The Raisin Cookie Model of the Atom . 35Summary ...................................................... 37Homework Problems .................................... 38

    2 The Nucleus .............412.1 Radioactivity ........................................ 412.2 The Planetary Model of the Atom ........ 452.3 Atomic Number .................................... 482.4 The Structure of Nuclei ........................ 522.5 The Strong Nuclear Force, Alpha Decay

    and Fission ............................................. 562.6 The Weak Nuclear Force; Beta Decay 582.7 Fusion .................................................. 612.8 Nuclear Energy and Binding Energies. 622.9 Biological Effects of Ionizing Radiation 652.10* The Creation of the Elements .......... 67Summary ...................................................... 69Homework Problems .................................... 70

    3 Circuits, Part 1 .........713.1 Current ................................................. 723.2 Circuits ................................................. 753.3 Voltage................................................. 763.4 Resistance ........................................... 803.5 Current-Conducting Properties of Materi-

    als ........................................................... 873.6 Applications of Calculus ..................... 90Summary ...................................................... 91Homework Problems .................................... 92

    4 Circuits, Part 2 .........954.1 Schematics .......................................... 964.2 Parallel Resistances and the Junction

    Rule ........................................................ 974.3 Series Resistances ............................ 101Summary .................................................... 105Homework Problems .................................. 106

  • 11Contents

    5 Fields of Force .......1095.1 Why Fields? ........................................1105.2 The Gravitational Field .......................1125.3 The Electric Field ................................1145.4 Voltage for

    Nonuniform Electric Fields ....... 1205.5 Field of a Continuous Charge

    Distribution ............................... 122Summary .....................................................119Homework Problems .................................. 120

    6 Electromagnetism .1276.1 The Magnetic Field ............................ 1286.2 Calculating Magnetic Fields

    and Forces ...................................... 1266.3 Induction ............................................ 1326.4 Electromagnetic Waves ..................... 1366.5 Calculating Energy in Fields .............. 1386.6* Symmetry and Handedness ............. 142Summary .................................................... 143Homework Problems .................................. 144Exercises .....................149Solutions ......................155Glossary .......................157Index .............................157

    +Supplements 4-7 and 4-8 are available online at

    www.lightandmatter.com.7 LRC Circuits7.1 Capacitance and Inductance7.2 Oscillations7.3 Voltage and Current7.4 Decay7.5 Impedance7.6 Complex Impedance8 Maxwell's Equations8.1 Maxwell's Equations8.2 The Curl, Formally8.3 The Divergence, Formally8.4 Methods of Attack

  • 12 Contents

  • 13

    Preface

    Who are you? However much you relate your identity to yourphysical appearance, you know that your personality ultimatelyresides in the unique arrangement of your brains electrical network.Mary Shelley may have conceived of electricity as a mystical lifeforce that could jerk the leg of a dead frog or animate Dr.Frankensteins monster, but we now know the truth is both moresubtle and more wonderful. Electricity is not the stuff of life but ofconsciousness.

    Evidence is mounting that the universe has produced vastnumbers of suitable habitats for life including, within our ownsolar system, a watery ancient Mars and the oceans that lie underthe icy surface of Jupiters moon Europa. But even as we debateclaims of fossilized Martian bacteria, a third generation of radioastronomers has found nothing but a wasteland of static in thesearch for extraterrestrial intelligence.

    Is life ubiquitous in the universe but consciousness rare? Interms of geologic time, it took a mere wink of an eye for life tocome into being on Earth once conditions were suitable, so there isevery reason to believe that it exists elsewhere. Large-brainedmammals, however, appear as a virtual afterthought in the record ofour biosphere, which remains dominated by single-celled life. Nowyou begin your study of electricity and magnetism, the phenomenaof which your own mind is made. Give some though to this imageof awesome loneliness: there may be no other planet in our galaxyof ten billion stars where a collection of electric charges and fieldscan ponder its own existence.

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  • 15

    1 Electricity and the AtomWhere the telescope ends, the microscope begins. Which of the twohas the grander view?

    Victor HugoHis father died during his mothers pregnancy. Rejected by her as a boy,

    he was packed off to boarding school when she remarried. He himself nevermarried, but in middle age he formed an intense relationship with a muchyounger man, a relationship that he terminated when he underwent apsychotic break. Following his early scientific successes, he spent the rest ofhis professional life mostly in frustration over his inability to unlock thesecrets of alchemy.

    The man being described is Isaac Newton, but not the triumphantNewton of the standard textbook hagiography. Why dwell on the sad sideof his life? To the modern science educator, Newtons lifelong obsessionwith alchemy may seem an embarrassment, a distraction from his mainachievement, the creation the modern science of mechanics. To Newton,however, his alchemical researches were naturally related to his investiga-tions of force and motion. What was radical about Newtons analysis ofmotion was its universality: it succeeded in describing both the heavens andthe earth with the same equations, whereas previously it had been assumed

  • 16

    that the sun, moon, stars, and planets were fundamentally different fromearthly objects. But Newton realized that if science was to describe all ofnature in a unified way, it was not enough to unite the human scale withthe scale of the universe: he would not be satisfied until he fit the micro-scopic universe into the picture as well.

    It should not surprise us that Newton failed. Although he was a firmbeliever in the existence of atoms, there was no more experimental evidencefor their existence than there had been when the ancient Greeks first positedthem on purely philosophical grounds. Alchemy labored under a traditionof secrecy and mysticism. Newton had already almost single-handedlytransformed the fuzzyheaded field of natural philosophy into somethingwe would recognize as the modern science of physics, and it would beunjust to criticize him for failing to change alchemy into modern chemistryas well. The time was not ripe. The microscope was a new invention, and itwas cutting-edge science when Newtons contemporary Hooke discoveredthat living things were made out of cells.

    1.1 The Quest for the Atomic ForceNewton was not the first of the age of reason. He was the last of themagicians...

    John Maynard Keynes

    Newtons questNevertheless it will be instructive to pick up Newtons train of thought

    and see where it leads us with the benefit of modern hindsight. In unitingthe human and cosmic scales of existence, he had reimagined both as stageson which the actors were objects (trees and houses, planets and stars) thatinteracted through attractions and repulsions. He was already convincedthat the objects inhabiting the microworld were atoms, so it remained onlyto determine what kinds of forces they exerted on each other.

    His next insight was no less brilliant for his inability to bring it tofruition. He realized that the many human-scale f